In-situ metalization monitoring using eddy current measurements during the process for removing the film

ABSTRACT

A method for measuring conductance of a sample using an eddy current probe with a sensing coil. The method includes N repetitions of measuring first and second voltage pairs including in-phase and quadrature components of an induced AC voltage in the sensing coil, calibrating the first signal based on the measured second signal at a different separation from the sample and reference material, determining a conductance function relating conductance with location along the selected curve, processing the calibrated first voltage pairs to generate a lift-off curve, determining an intersection voltage pair representing intersection of the lift-off curve with a selected curve, and determining the conductance of the sample from the intersection voltage pair and the conductance function.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of application Ser. No. 10/166,585,filed Jun. 5, 2002, now U.S. Pat. No. 6,621,264 entitled “IN-SITUMETALIZATION MONITORING USING EDDY CURRENT MEASUREMENTS DURING THEPROCESS FOR REMOVING THE FILM” in the name of Lehman et al., which is adivisional of application Ser. No. 09/633,198, filed Aug. 7, 2000, nowU.S. Pat. No. 6,433,541 entitled “IN-SITU METALIZATION MONITORING USINGEDDY CURRENT MEASUREMENTS DURING THE PROCESS FOR REMOVING THE FILM” inthe name of Lehman et al. The above-identified applications Ser. Nos.09/633,198 and 10/166,585 claim the benefit of U.S. ProvisionalApplication No. 60/172,080, filed Dec. 23, 1999 entitled “IN-SITUMETALIZATION MONITORING USING EDDY CURRENT MEASUREMENTS” in the name ofLehman et al. applications Ser. Nos. 60/172,080, 09/633,198, and10/166,585 are incorporated herein by reference in their entirety forall purposes.

BACKGROUND OF THE INVENTION

The invention relates to apparatus for performing measurements of filmcharacteristics (e.g., film endpoint detection and thickness) of asemiconductor wafer during a fabrication process, such as chemicalmechanical polishing (CMP) and chemical vapor deposition.

Two approaches to measuring a top-layer film thickness are thefour-point probe and scanning electron microscopy (SEM) methods. Thefour-point method includes forming multiple contacts with the wafersurface to obtain a conductivity measurement. The SEM method includescross-sectioning the wafer to thereby obtain the film thickness throughcommon SEM imaging techniques. Although the four-point probe and SEMmethods may provide adequate film measurements, these tests may only beperformed on monitor wafers since these methods destroy the wafer duringthe measurement process.

One non-destructive measurement approach is to obtain opticalmeasurements of the film thickness, e.g., via optical reflectance ortransmission measurements. In-situ optical measurements are typicallynot performed during a CMP process because the sample undergoingpolishing is obscured by debris that may adversely affect themeasurement reading. The wafer is polished by rubbing the wafer betweena wafer carrier and pad that is atop a platen. A slurry is typicallyused to mechanically and chemically facilitate removal of a portion of afilm deposed on the wafer's surface. The CMP slurry and residuesadjacent to the wafer surface are typically optically inhomogeneous andmostly opaque.

This debris (e.g., slurry and film residue) typically interferes withmeasurements of the sample. In a polishing process, it is desirable todetect when a film has been removed from the wafer, either entirely orto a specific thickness. When the film is removed, this is usuallyreferred to as the endpoint. It is important to detect the endpoint sothat the wafer is not over polished. For example, in copper CMP, thecopper film is initially optically opaque. Typically, three endpointsare detected in copper CMP. A first endpoint may occur when the copperfilm is reduced to a specific thickness, which may be, for example, whenthe copper film begins to become optically transparent. Second, it isdetermined when the copper is completely removed so that the underlyingliner layer (e.g., TaN or WN) is exposed. Finally, it is determined whenthe liner layer has been removed.

When the endpoint of a film is reached, the polishing can then bestopped without polishing away other structures on the wafer or tochange process conditions. Since there is a lot of debris (e.g., slurryand/or film residue) associated with the CMP process, it would bedifficult to accurately measure the endpoint while the wafer isundergoing CMP.

Although various approaches to performing in situ optical measurementduring CMP have been proposed, none of these approaches solve theproblem of debris obscuring the wafer. Of note, U.S. Pat. No. 5,433,651describes a single beam reflectometer employing a window within a cavityof the CMP polishing pad and platen. The described approach has thedisadvantage that CMP slurry and residue can build up in the cavityformed within the platen/polishing pad. The slurry and residue makeoptical measurements difficult. Another approach, described in E.P.Patent 96302176.1, attempts to solve this problem by providing a “softwindow” within the cavity where slurry and residue might otherwiseaccumulate. Unfortunately, this window typically becomes scratchedduring the polishing process and pad conditioning and thereby alsodegrades the quality of optical measurements. Also, the material that isused to form the soft window typically scatters the measuring beam.

U.S. Pat. No. 5,081,796 describes moving a small edge portion of thewafer off the edge of the polishing pad, where the removed portion isthen exposed to a jet of water which helps guide a beam onto the wafer'sedge. However, this approach has the disadvantage of only measuring thefilm at the edge of the wafer. Since only a small portion of the entirewafer surface is measured, measurement of the endpoint is not veryaccurate. Furthermore, this procedure may adversely affect the polishingprocess.

An alternative approach to performing in situ optical CMP measurementsis described in above referenced co-pending Ser. No. 09/396,143 filedSep. 15, 1999 entitled “APPARATUS AND METHODS FOR PERFORMINGSELF-CLEARING OPTICAL MEASUREMENTS” by Nikoonahad et al, whichapplication is incorporated herein by reference in its entirety for allpurposes. Although this approach works well for measuring thin films,optical measurements are inadequate for measuring thick films.

Additionally, current approaches for estimating the duration for a filmto be removed are inaccurate. That is, the polishing time tends to varysignificantly from wafer to wafer. Thus, a significant amount ofadditional time is added to the polishing time estimate to account forwide variations in polishing time. Although this approach tends toassure that a film will be adequately removed, of course, this approachalso adversely affects thorough-put.

Another non-destructive measurement technique utilizes an eddy currentprobe. One such technique is described in U.S. Pat. No. 6,072,313 by Liet al. This patent describes an eddy current probe that merely detectswhether a film has changed. More specifically, the disclosed eddycurrent probe is formed from a high-Q tuned resonant circuit. Thisapproach has several associated disadvantages. For example, the high-Qresonant circuits are sensitive to environmental changes, and thereforethe eddy probe measurements are detrimentally affected by disturbancesin environmental conditions, such as temperature, vibration, and changesin distances between the probe and the wafer. Additionally, onlymagnitude measurements at a single resonant frequency are provided. Insum, present approaches provide a relatively limited amount ofinformation about the film under test.

Accordingly, there is a need for improved in-situ techniques andapparatus for providing information regarding a film while such film isundergoing a deposition or removal process. More specifically, there isa need for non-destructive techniques and apparatus for accurately andefficiently measuring film thickness and/or detecting a film's endpoint.

SUMMARY OF THE INVENTION

Accordingly, the present invention addresses some of the above problemsby providing improved apparatus and methods for providing informationregarding a film while such film is undergoing a deposition or removalprocess. Specifically, improved mechanisms for performing in-situ eddyprobe measurements are disclosed.

In one embodiment, the invention pertains to a method of obtaininginformation in-situ regarding a film of a sample using an eddy probeduring a process for removing the film. The eddy probe has at least onesensing coil. An AC voltage is applied to the sensing coil(s) of theeddy probe. One or more first signals are measured in the sensingcoil(s) of the eddy probe when the sensing coil(s) are positionedproximate the film of the sample. One or more second signals aremeasured in the sensing coil(s) of the eddy probe when the sensingcoil(s) are positioned proximate to a reference material having a fixedcomposition and/or distance from the sensing coil. The first signals arecalibrated based on the second signals so that undesired gain and/orphase changes within the first signals are corrected. A property valueof the film is determined based on the calibrated first signals.

In one aspect, the property value is a thickness value. In a specificimplementation, the reference material is a sample carrier that holdsthe sample. Preferably, one or more third signals are measured in thesensing coil of the eddy probe when the sensing coil is not near anysample or reference materials, and calibration of the first signals isfurther based on the third signal. In one implementation, thecalibration of the first signals results in compensation of gain and/orphase errors caused by a temperature change or a change in distancebetween the eddy probe and the reference material.

In another embodiment, a measurement device for obtaining informationregarding a film of a sample is disclosed. The measurement deviceincludes an AC voltage source and a sensing coil coupled with the ACvoltage source so that the AC voltage source is operable to induce an ACvoltage on the sensing coil. The measurement device also includes animpedance meter coupled with the sensing coil that detects a change inthe AC voltage on the sensing coil, a memory having programminginstructions, and a processor coupled with the memory. The processor andmemory are adapted for causing the AC voltage to be induced on thesensing coil and analyzing the change in the AC voltage on the sensor todetermine a thickness value of the film of the sample. In a specificimplementation the processor and memory are further adapted to performthe above described methods.

In another aspect of the invention, a chemical mechanical polishing(CMP) system for polishing a sample with a polishing agent andmonitoring the sample is disclosed. The CMP system includes a polishingtable, a sample carrier arranged to hold the sample over the polishingtable, and a measurement device as described above. The polishing tableand sample carrier are arranged to receive a polishing agent between thesample and the polishing table and to polish the sample by moving thepolishing table and the sample carrier relative to each other. Themeasurement device is arranged to obtain information regarding thesample while the sample is being polished.

These and other features and advantages of the present invention will bepresented in more detail in the following specification of the inventionand the accompanying figures which illustrate by way of example theprinciples of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be readily understood by the followingdetailed description in conjunction with the accompanying drawings,wherein like reference numerals designate like structural elements, andin which:

FIG. 1 is a diagrammatic representation of a chemical mechanicalpolishing (CMP) system having an eddy measurement device or probe inaccordance with one embodiment of the present invention;

FIG. 2 is a simplified equivalent circuit of an eddy circuit inaccordance with one embodiment of the present invention;

FIG. 3A is a graph of an output of the eddy probe of FIG. 2 as afunction of time in accordance with one embodiment of the presentinvention;

FIG. 3B is a graph of a calibrated magnitude output of the eddy probe ofFIG. 2 as a function of time in accordance with one embodiment of thepresent invention;

FIG. 3C is a vector plot of the measured voltage vectors (I vs. Q) ofthe eddy probe of FIG. 2;

FIG. 3D is a plot of measured copper thickness vs. time during a polishprocess.

FIG. 4 is a graph of eight lift-off curves, and a circular arcintersecting the lift-off curves, generated in accordance with oneembodiment of the present invention;

FIG. 5 is side view of a combination eddy current and opticalmeasurement device in accordance with another embodiment of the presentinvention;

FIG. 6 is a diagrammatic representation of a section of a chemicalmechanical polishing (CMP) apparatus that incorporates one or moremeasurement system(s) (not shown) with a self-clearing objective inaccordance with one embodiment of the present invention;

FIG. 7 shows four graphs of reflectivity values as a function of filmthickness;

FIG. 8A illustrates three layers of a sample: a silicon dioxide layer, aTa layer, and a Cu layer;

FIG. 8B illustrates the results after polishing the Cu of FIG. 8A at arelatively fast rate;

FIG. 8C illustrates dishing and erosion within the Ta layer as a resultof a relatively fast rate of polishing for the Cu layer;

FIG. 8D illustrate a slow etch of a copper layer; and

FIG. 9 is a diagrammatic illustration of a multi-chamber deposition toolhaving a combination eddy current and optical probe in accordance withone embodiment of the present invention.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

Reference will now be made in detail to the specific embodiments of theinvention. Examples of these specific embodiments are illustrated in theaccompanying drawings. While the invention will be described inconjunction with these specific embodiments, it will be understood thatit is not intended to limit the invention to the described embodiments.On the contrary, it is intended to cover alternatives, modifications,and equivalents as may be included within the spirit and scope of theinvention as defined by the appended claims. In the followingdescription, numerous specific details are set forth in order to providea thorough understanding of the present invention. The present inventionmay be practiced without some or all of these specific details. In otherinstances, well known process operations have not been described indetail in order not to unnecessarily obscure the present invention.

Since electrical resistivity is the inverse of electrical conductivity,determination of either of these quantities in accordance with theinvention determines both of them. Although for simplicity, theinvention is described herein with reference to embodiments whichdetermine a sample's electrical conductivity, it will be apparent tothose of ordinary skill in the art how to implement variations on theseembodiments to determine electrical resistivity in accordance with theinvention. It will also be apparent to those of ordinary skill in theart how to implement variations on these embodiments to determinecomplex electrical conductance, resistance, sheet conductance, or sheetresistance. For example, electrical resistance can be determined bymeasuring electrical resistivity using the described apparatus,independently measuring a linear dimension of the sample by anyconventional means, and dividing the measured resistivity by themeasured linear dimension to determine the resistance. In the claims andthe abstract, the term “conductance” is used in a broad sense to denoteconductivity, resistivity, conductance, resistance, sheet conductance,or sheet resistance.

The expression “AC voltage” is used throughout the specification,including in the claims, to denote any periodically time-varyingvoltage, including for example, voltages having sinusoidal, square wave,or sawtooth waveforms.

In general terms, several embodiments of the present invention provideimproved mechanisms for performing in-situ eddy current measurementsand/or optical measurements. That is, the eddy current measurementapparatus and techniques of the present invention may be utilized aloneor in combination with the optical apparatus and techniques of thepresent invention. Likewise, the optical apparatus and techniques of thepresent invention may be used with or without the eddy current apparatusand techniques.

Referring initially to a novel eddy current system, FIG. 1 is adiagrammatic representation of a chemical mechanical polishing (CMP)system 100 having an eddy measurement device or probe 102 in accordancewith one embodiment of the present invention. As shown, the eddy probe102 is mounted within the polisher platen 110 beneath the pad 106. TheCMP system 100 also includes a wafer carrier 104 to which a wafer may bemounted (not shown). As is well known to those skilled in the art, theplaten 110 and pad 106 move relative to the wafer carrier to therebypolish the mounted wafer. As a result of such movement, the eddy probe102 may obtain measurements of the wafer, wafer carrier, and/or freespace as the platen 110 moves relative to the wafer carrier 110. Asdescribed below, eddy probe measurements of the wafer carrier and/orfree space may be utilized to calibrate the eddy probe measurements ofthe wafer and thereby minimize environmental effects.

The eddy probe 102 is preferably coupled with processor 108 thatincludes a general purpose digital computer programmed with software forgenerating the data signals described herein (for example signalsindicative of the below-described conductance function and related filmthickness, and signals indicative of the below-described conductivity orresistivity values and related thickness values), and for storing datain (and retrieving stored data from) memory associated therewith. Ofcourse, any suitable combination of hardware and/or software may beutilized for controlling the eddy probe 102 and analyzing signalsmeasured by the probe 102.

The eddy probe circuit may be implemented in any suitable manner. Ingeneral terms, the eddy probe includes a sensing coil, an AC voltagesource for inducing an AC voltage on the sensing coil, and an impedancemeter for measuring an impedance or impedance change on the sensingcoil. The impedance meter may take the form of any suitable meter formeasuring the real and imaginary components of the sensing coilimpedance. Alternatively, the impedance meter may include a bridgecoupled with the sensing coil, as well as a reference coil, and asynchronous detector as described below with reference to FIG. 2.

FIG. 2 is a simplified equivalent circuit of an eddy probe circuit 200in accordance with one implementation of the present invention. The eddyprobe circuit 200 includes differential probe coils 202 mounted within aprobe head 203. The differential coils 202 include a sensing coil 202 bpositioned close to the sample and a reference coil 202 a positionedaway from the sample. In one embodiment, the probe head 203 is mountedwithin the platen of the CMP system (not shown). The eddy probe circuit200 also includes an impedance bridge 204 coupled with differentialprobe coils 202. The impedance bridge 204 is also coupled with asynchronous detection block 250 for measuring the I and Q differencevalues of the differential probe coils 202. The differential probe coils202 are also driven by frequency source 208 through power amp 206 andbridge 204.

When activated, frequency source 208 produces AC voltage in differentialprobe coils 202 with a selected frequency within the range from 1 KHz toat least 100 MHz. In a typical case in which differential probe coils202 (and associated electrical lines) represent a load of 50 ohms tosource 208, source 208 is capable of producing sinusoidal voltage havinga peak-to-peak amplitude of about five volts in differential probe coils202. To increase the probe's spatial resolution, thereby allowingmeasurement of the conductance of smaller sample regions (either at thesample surface or at selected depths below the sample surface), thediameters of differential probe coils 202 should be reduced and the ACvoltage frequency in differential probe coils 202 increased.Additionally, the AC voltage frequency may be selected based on anysuitable factor. For example, the frequency may be selected fordifferent film thicknesses, material composition, probe-to-carrierdistance, and/or probe size. A sweep of frequencies or severalsimultaneous discrete frequencies may also be selectably generated onthe eddy probe.

Desired thin layers of a multilayer sample can be selectively measuredbecause, for a given probe, the depth of the sample region measureddepends in a well understood manner on the AC voltage frequency indifferential probe coils 202. The differential coil voltage frequencycan be chosen to cause the electromagnetic field due to the differentialcoil to extend to a desired depth in the sample.

For a given separation between the lower end of sensing coil 202 b andsample 205, the amplitude of the AC voltage induced in sensing coil 202b in response to AC voltage in sensing coil 202 b will depend on theconductance of sample 205. Differential amplifier 210, which isconnected to differential probe coils 202, amplifies the differencebetween the signals from the reference coil 202 a and the sensing coil202 b. By taking a difference between the reference coil 202 a and thesensing coil 202 b, differences caused by environmental changes to thecoils may be reduced since these changes, in theory, affect both coilsabout equally. Alternatively, a single probe coil could be used. Thisdifference signal contains an in-phase component and the quadraturecomponent. The output of the differential amplifier 210 is input into afirst mixer 214, along with the AC voltage output from source 208. Theoutput of the amplifier 210 is also input to a second mixer 216, alongwith the AC voltage that has first been phase shifted by 90 degrees. Theoutput of mixer 214 is input to a low pass filter 218, and the output ofmixer 216 is output to a low pass filter 220. The output of the low passfilters are the separated in-phase (I) and quadrature (Q) components ofthe differential probe coils 202. These signals are then sent throughanalog-to-digital converters 222 and 224, respectively, to generatedigital I and Q values. Alternative methods for detecting I and Qcomponents could also be used.

In order to provide high sensitivity to thin conducting films, it isdesirable that amplifier 210 be selected to provide a high gain (on theorder of 10,000 to 50,000). To avoid signal saturation, such high gainscan only be used if the bridge circuit 204 is precisely balanced, sothat the bridge voltage output is effectively near zero when no sampleis present proximate the sensing coil 202 b. As it is currentlydifficult to construct the differential probe coil assembly 202 suchthat the two coils are electrically identical, it is necessary to adjustthe impedance of either the fixed bridge elements 204 or of the probecoils 202. The impedance of the fixed bridge or probe coils may bebalanced by any suitable impedance adjustment mechanism. For example, avariable resistance may be added in series with either probe coil 202 oreither bridge resistor 204. The imaginary impedance term may be balancedby placing a small capacitance across either probe coil 202 or eitherbridge resistor 204. The resistive and capacitive elements used tobalance the bridge circuit just described may take the form of discretecomponents that are manually adjusted, or they may be replaced withactive elements such as electronically variable resistors and variablecapacitance diodes or varactors, which may be used to dynamicallybalance the bridge circuit either under computer control or viaclosed-loop control circuitry. Of course, if it becomes possible toconstruct the differential probe coil assembly 202 such that the twocoils are electrically identical, it may become no longer necessary toadjust the impedance of either the fixed bridge elements 204 or of theprobe coils 202.

Thus, the output signals from synchronous detection block 250,preferably a digital signal indicative of the amplitudes of both thein-phase and quadrature components of the induced voltage indifferential probe coils 202, undergoes processing in accordance withthe invention in processor 108 of FIG. 1 (in a manner to be describedbelow). In sum, the in-phase and quadrature components of the inducedvoltage in differential probe coils 202 are measured using an ACmutual-inductance bridge. An alternative eddy current circuit isdescribed in U.S. Pat. No. 5,552,704 by Mallory et al filed 25 Jun.1993, which patent is herein incorporated by reference in its entirety.

The bridge design provides some protection against environmental changesto the probe during measurements. That is, the bridge is relativelyimmune to variable environmental conditions. In some preferredembodiments, each coil is wound on a core of material, such as aconductive epoxy or high permeability ferrite material, that alsominimizes environmental effects and improves signal-to-noise. In otherpreferred embodiments, each coil is wound on a core of acrylic material.The differential probe and bridge design also provides a sensitiveimpedance measurement of the sensing coil 202 b relative to thereference coil 202 a. That is, the absolute impedance of the sensingcoil 202 b as affected by a sample may be obtained. In other words,there is a quantifiable measurement.

As explained below, the absolute impedance values can be directlycorrelated to absolute thickness values. Accordingly, precise removalrates may also be determined. Previous eddy probe methods are capable ofonly determining that thickness had changed, but are not capable ofdetermining by how much the thickness has changed. That is, conventionalmethods cannot isolate the area of interest from environment inducedchanges. Thus, conventional methods required extensive calibration andpriori knowledge of the process and sample.

Additionally, the probe 203 may be easily scaled down to obtain a smallspot size. Thus, when the size of the differential probe is reduced, asmaller, but usable, signal may still be detected by the differentialprobe.

As described above, the eddy current measurement techniques of thepresent invention may be utilized in various types of in-situapplications. For example, an eddy current probe may be integratedwithin a chemical mechanical polishing (CMP) tool. In this application,the eddy current probe is utilized to detect one or more endpoint(s) ofone or more etched layers. By way of another example, an eddy currentprobe may be integrated within a deposition tool. In this case, the eddyprobe is utilized to detect film thickness of a deposited layer.

Turning first to the CMP application, techniques for determining filmthickness of a sample undergoing CMP using an eddy probe are provided.These mechanisms may also be used to determine temperature and thedistance between the probe and sample. In general terms, phase andmagnitude measurements for the sample under test, sample carrier, andfree space are obtained. The measurements of the sample carrier and/orfree space may be utilized to calibrate the measurements taken of thesample under test. In general terms, the measurements of the samplecarrier and/or free space (or open coil) are used to compensate for gainand phase errors within the measurements of the sample's film thickness.

The sample carrier is typically formed from a conductive material(encased in plastic) that surrounds the sample, and the composition andthickness of the sample carrier is expected to remain constant. Thus, ameasurement of the sample carrier provides a stable reference point forcontinuously calibrating the measurement of the sample. The measurementof the reference also provides a mechanism for determining the distancefrom the probe to the carrier (e.g., as a measurement of pad thickness).Of course, any suitable reference material may be used, and thereference material may be placed at any measurable position. Forexample, a slug of conductive material may be mounted behind the wafercarrier. A measurement of free space provides a mechanisms for sensingchanges to the detection circuitry (e.g., change in coil temperature,etc.).

FIG. 3A is a graph of an output of the eddy probe (e.g., real orimaginary component) of FIG. 2 as a function of time in accordance withone embodiment of the present invention. The probe moves relative to thewafer and wafer carrier so that measurements are sequentially andrepeatedly taken across the wafer, wafer carrier, and free space.Preferably, the probe is positioned so that it moves radially across thewafer. Referring to FIG. 3A, measured peak signal values for the samplecarrier are shown at data points 234, 434, and 634 (in this example,each data point is 1 ms). The peak signal values for free space (or opencoil) are shown at data points 212, 412, and 612. The peak signal valuesfor a center point on the sample are shown at data points 310, 510, and710.

Reference vectors (e.g., for the carrier) may then be defined as:REF(I, Q)=(R _(i) −OC _(i) , R _(q) −OC _(q))  [1]

R_(i) is the I component for the sample carrier signal, and R_(q) is theQ component for the sample carrier signal. Likewise, OC_(i) is the Icomponent for the open coil or free space signal, and OC_(q) is the Qcomponent for the open coil or free space signal. The wafer vectors maythen be defined as:WAF(I, Q)=(W _(i) −OC _(i) , W _(q) −OC _(q))  [2]W_(i) is the I component for the wafer signal, and W_(q) is the Qcomponent for the wafer signal.

By comparing the sample and reference measurements, variations due totemperature and probe-to-carrier distance (as well as other types ofvariation) can be largely removed from the final calibrated magnitudeand phase values. For example, temperature changes cause the peak signalfor the carrier signal to drift down over time. This change in signalresulting from a temperature change is subtracted out of the wafer peaksignal by noting the drift in open coil and reference signals. Likewise,a change in probe-to-carrier distance will cause a change in thedifference between the open coil and carrier peak signals. This changein signal may also be compensated in the wafer signal.

Since measurements are quickly obtained with the differential coil andbridge arrangement, the calibrated magnitude and phase values may bequickly generated “on-the-fly” during the CMP process. These calibratedvalues may then be analyzed to readily determine various characteristicsregarding the sample.

FIG. 3B is a graph of a calibrated magnitude output of the eddy probe ofFIG. 2 as a function of time in accordance with one embodiment of thepresent invention. The magnitude values (on the vertical axis) may thenbe easily converted to thickness values to generate a film thicknessvalues as a function of time. For example, a sample having a knownthickness value may be measured with the eddy probe to generate a linearfunction of thickness as a function of voltage. Alternatively, thethickness of a sample measured with the eddy probe may be determinedwith any suitable measurement system, such as a four-point probe.Magnitude/thickness vs. voltage graphs may be generated for multiplesamples having known film thickness values and compositions. Thus, ameasured voltage value from a sample having an unknown thickness may becorrelated with a thickness value via thickness vs. voltage graphs.

A wealth of information is provided by measuring both the phase andmagnitude at multiple positions (e.g., a carrier position, multiplewafer positions, and an open coil position). For example, therelationships between the different measured vectors (e.g., reference,wafer, and open coil vectors) may be graphically illustrated. Forexample, changes in the film thickness can be separated from changes inprobe-to-sample distance and temperature effects by examining the realand imaginary changes in the probe coil impedance, along with thecarrier and open coil measurements. FIG. 3C is a graph of each of themeasured vectors (I vs. Q). Various environmental conditions cause thevectors to drift within the graph in a particular manner. As shown, atemperature change causes the vectors to move towards the origin point.In contrast, an increase in probe-to-carrier distance causes a decreasein the carrier signal's magnitude. The measurement vector direction isalso affected by the material composition. For example, ferrous vs.non-ferrous metals may be easily discerned.

Changes in temperature and/or probe-to-sample distance values mayindicate a problem within the CMP system. For example, a significantdecrease in probe-to-carrier distance may indicate that the pad of theCMP system requires replacement. By way of another example, asignificant increase in temperature may indicate that the CMP system isoverheating and corrective action is required. The temperature changemay also be used to estimate endpoint. For example, as copper isremoved, the friction coefficient of the copper changes, which changeresults in a change in the amount of heat generated by the copperrubbing against the pad and slurry. This change in temperature may thenbe directly correlated with the endpoint.

Additionally, variations (e.g., variations in polishing rates,temperature, etc.) across the sample may also be determined duringpolishing and utilized to adjust the process on the fly (e.g., tomaintain uniformity). For example, if one portion of the sample ispolishing at a slower rate than the rest of the sample, adjustments tothe polishing parameters may be made to increase the polishing rate tothe slower polishing sample portion. The adjustment techniques depend onthe particular configuration of the polishing system. For instance, airbladders may be mounted behind the sample carrier to provide backpressure to the sample against the pad. Pressure may be increased to aparticular sample portion by increasing the air content of one or morebladders located behind the particular sample portion. Thus, film may beremoved uniformly across the sample. Other types of CMP systems maysimply provide air holes or vacuum holes behind the wafer forcontrolling pressure. In these configurations, the amount of air orvacuum is simply decreased or increased to particular sample portionsbased on the level of unevenness in polishing rates.

The use of time history and spatially diverse measurements across thesample (e.g., radial measurements of thickness) gives a filler coverageand better confidence level for determining endpoints. One can use thetime history to determine the polishing rate, and the remainingthickness to determine the endpoints. The radial non-uniformity can alsobe determined and accounted for in the prediction of endpoints and/orpolishing rate. Hence, a relatively high confidence level for endpointprediction is obtained.

The techniques of the present invention for monitoring various processparameters (e.g., temperature change, probe-to-sample distance,polishing rate, etc.) may be combined with any suitable conventionalmonitoring techniques. For example, techniques for monitoring motorcurrent, torque, and motor ultrasonics may be used in conjunction withthe techniques of this invention to more accurately adjust operatingparameters of the CMP process.

The reported variations in polishing rate may also be used to estimatethe time required to reach a film's endpoint. For example, FIG. 3Dillustrates three different polishing rates for three different sampleportions. The difference in endpoints for each sample portion isdepicted by arrow 375. A polishing time that is long enough to reach theendpoint for all three sample portions may then be selected (i.e., thelongest polishing time).

Several eddy measurement analysis techniques are described in detailwithin U.S. Pat. No. 5,552,704 by Mallory et al filed 25 Jun. 1993,which patent is herein incorporated by reference in its entirety. Thispatent generally describes methods and apparatus for performingconductance measurements on a sample using an eddy current probe,without the need for measurement or knowledge of the separation betweenthe probe and the sample. This eddy current analysis technique will nextbe described with reference to FIG. 4. Initially, look-up table data isgenerated (by operating processor 108) and the data is stored (in memory108) as a look-up table for use in subsequent measurements on sampleshaving unknown conductivity.

To generate the look-up table data, eddy current measurements are firstperformed on each of a number of samples (N samples) having knownconductivity, to generate a corresponding number of lift-off curves (Nlift-off curves). Eight such lift-off curves are shown in FIG. 4.

Each lift-off curve is generated by producing an AC voltage indifferential coil 202 while measuring both the in-phase and quadraturecomponents of the difference AC voltage induced in differential coils202, for each of a number of probe positions along the z-axis. Theseparation between the sample and the probe (along the z-axis) need notbe measured or otherwise known.

Typically, a small number (such as twenty-five) of coil voltage pairs(each pair comprising an in-phase difference voltage and a correspondingquadrature difference voltage) are measured for each sample. Each coilvoltage pair is measured with a different probe position along thez-axis with respect to the sample. For each sample, a set of measuredcoil difference voltage pairs is processed to determine a lift-offcurve.

Specifically, for a given sample, processor 108 processes an outputsignal from synchronous detection block 250 (indicative of adifferential coil 202 voltage pair) for each of several probe positionsto determine a polynomial function (a function of “in-phase” voltageversus “quadrature” voltage) which best fits the data. This functiondetermines the lift-off curve for the sample.

An example of such a lift-off curve is the curve labeled “A” in FIG. 4.Lift-off curve A is determined by processing a number of sense coilvoltage pairs (e.g., seven sense coil voltage pairs) obtained bymeasuring a sample having a known resistivity of 0.0216 ohms per square.Lift-off curve R is a graph of a polynomial function of formY=−(K)−(L)X+(M)X.sup.2, where Y is quadrature voltage in units of Volts,X is in-phase voltage in units of Volts, and K, L, and M are constants.Processor 108 identifies this second order polynomial function as theone which best fits the measured voltage pairs.

In most cases, twenty-five (or a number on the order of twenty-five)sense coil voltage pairs are sufficient to characterize each lift-offcurve with adequate precision. The range of probe positions (along thez-axis) over which measurements are made is proportional to the sample'sconductivity (greater probe-to-sample separations are generally requiredfor samples of greater conductivities), and depends also on the proberadius. As a rule of thumb (for a typical sample), the maximumprobe-to-sample separation needed to determine a lift-off curve issubstantially equal to 50% of the drive coil radius. We prefer todiscard (or avoid measuring) sense coil voltage pairs for very largeprobe-to-sample separations, to avoid unnecessary processing of datathat will not contribute significantly to an accurate lift-off curvedetermination.

Returning to the FIG. 4 example, each of lift-off curves A through H isdetermined by the same process employed to determine above-describedcurve A (one lift-off curve A through H for each of eight samples havinga different known resistivity). The sample resistivities (in ohms persquare) associated with curves A through H, respectively, are 0.0216,0.0263, 0.0525, 0.0699, 0.081, 0.16, 0.2597, and 0.39.

After determining a set of reference lift-off curves (e.g., curves A-Hshown in FIG. 4), processor 108 then determines a set of “intersection”voltage pairs, each intersection voltage pair representing theintersection of a different one of the reference lift-off curves with a“selected” curve (which can be, for example, a circular arc or anothergraph of a polynomial function) in X-Y voltage space, where X representsin-phase voltage and Y represents quadrature voltage. One such “selectedcurve” (circular arc V) is shown in FIG. 2. Selected curve V is asemicircle centered at X=0 volts and approximately Y=−0.8 volts.Alternatively, another selected curve could have been employed, such asa circular arc centered at the origin (Y=0 volts, X=0 volts). The “X,Y”coordinates of point A1 along lift-off curve A are an example of such anintersection voltage pair for “selected” curve V.

After processor 108 determines a set of intersection voltage pairs alonga selected curve, processor 108 implements the next step of theinventive method which is to determine a functional relation between theknown conductivity associated with each intersection voltage pair andthe selected curve (referred to below as a “conductance function”). Theconductance function determines a conductivity value for each point onthe selected curve, including conductivity values not associated withany of the reference lift-off curves. For example, point Z on selectedcurve V corresponds to a unique conductivity (determined by processor108 from the conductance function for selected curve V) that is greaterthan 0.0263 ohms per square (associated with lift-off curve B) and lessthan 0.0525 ohms per square (associated with lift-off curve C). In aclass of preferred embodiments, processor 108 stores a conductivityvalue, determined by the conductance function, for each of manydifferent points (index voltage pairs) on the selected curve in memory108 as a look-up table. Each such conductivity value can be retrievedfrom the stored look-up table by accessing the memory location indexedby the corresponding index voltage pair.

In variations on the described method, a conductance function relating aknown conductance (rather than a conductivity) of each measured sampleto an intersection voltage pair on the “selected” curve, or a“resistance function” or “resistivity function” relating a knownresistance or resistivity of each measured sample to an intersectionvoltage pair on the “selected” curve, can be determined and processed asa substitute for the above-described conductance function. Forconvenience, the expression “conductance function” is used herein(including in the claims) in a broad sense to denote any suchconductance function, resistance function, or resistivity function, orany function which relates a known conductance, conductivity,resistance, resistivity, sheet resistance, or sheet conductance of eachof a set of measured samples to an intersection voltage pair on a“selected” curve, as well as a narrowly defined conductance function(relating a known conductance of each of a set of measured samples to anintersection voltage pair on a “selected” curve).

Although the eddy probe is preferably located within the platen, it mayalso be located within the backside of the sample carrier. In thisarrangement, the carrier no longer provides a reference signal. Thus, atemperature sensor is also preferably mounted to the carrier so that themeasured sample signals may be calibrated for any temperature changes. Areference metal slug (encased in plastic) may also be positioned toperiodical move past the probe so that a reference signal for a knownsample may be obtained. In this configuration, the bridge probe designalso allows relatively small spot size measurements, as compared with aresonator probe design.

The CMP system may also include any suitable optical measurement device,in addition to the eddy probe. Since eddy current measuring devices workwell with thick films and optical measuring devices work better withthin films, a broad range of film thickness may be measured by combiningan eddy device and an optical device. FIG. 5 is side view of acombination eddy current and optical measurement device 500 inaccordance with another embodiment of the present invention. As shown,the combination measurement device 500 is integrated within a CMP tool.In the illustrated embodiment, a fiber optic measuring device 504 and aeddy current probe 502 (e.g., as described above) are housed withinhousing 510. Housing 510 is formed from a material that is substantiallytransparent the eddy current signals and optical signals. For example,the housing is formed from glass.

The optical device may be integrated within the CMP tool in any suitablefashion so that accurate optical measurements may be obtained. Forexample, the eddy probe coils may be wrapped around the optical element.Preferably, the optical measurement device is positioned separatelywithin the platen from the eddy probe system. Alternatively, the eddyprobe may be positioned behind the wafer as described above. In oneembodiment, a self-clearing objective is inserted within the platen andpad of the CMP tool for the optical measurement device. Opticalmeasurements may be made through the self-clearing objective during CMPoperation. Several embodiments of the self-clearing objective isdescribed in the above referenced co-pending U.S. patent applicationsSer. No. 09/396,143 filed 15 Sep. 1999 entitled “Apparatus and Methodsfor Performing Self-Clearing Optical Measurements” by Nikoonahad et al.and Ser. No. 09/556,238 filed 24 Apr. 2000 entitled “Apparatus andMethods for Detecting Killer Particles During Chemical MechanicalPolishing” by Nikoonahad et al. These applications have assignmentrights in common and are incorporated herein in their entirety.

FIG. 6 is a diagrammatic representation of a section of a chemicalmechanical polishing (CMP) apparatus 600 that incorporates one or moremeasurement system(s) (not shown) with a self-clearing objective inaccordance with one embodiment of the present invention. The dimensionsof the various components are exaggerated to better illustrate theself-clearing objective of this invention. As shown, the CMP apparatus600 includes a sample holder 601 and a pad 607 and a platen 606 having ahole 608. The sample holder 601 is arranged to hold a sample 602 againstthe pad 607 and the platen 606. A slurry 604 is placed between thesample 602 and pad 607, which is atop platen 606. When the sample ismoved relative to the pad 607, the slurry 604 functions to mechanicallyand/or chemically polish the sample 602. Of course, any suitablepolishing agent may be utilized.

The hole 608 of the pad 607 and platen 606 is configured to contain aself-clearing objective. The self-clearing objective of FIG. 6 includesan optical element 610 and a flowing fluid 613. Any suitable mechanismmay be implemented for generating the flowing fluid 613 of theself-clearing objective. As shown, the self-clearing objective alsoincludes a fluid pump 612 and a fluid outlet 614 that generate aconstant fluid flow between the optical element 610 and sample surface602. Alternatively, a fluid pumping system may be implemented within asingle device that generates flowing fluid 613. By way of a finalexample, a ring-shaped hole may be formed around the viewing area intothe center of which the fluid is pumped. The fluid then exits throughthe ring-shaped hole.

The fluid pump 612 may include a control valve (not shown) for adjustingthe flow rate. Likewise, the fluid outlet 614 may include a vacuum thatprovides some control over the fluid flow rate to the fluid outlet 614.The fluid flow rate may be adjusted for different applications orpolishing conditions in order to provide different levels of clearingdepending upon the specific application. For example, the fluid flowrate may depend on type of slurry, polishing speed, size of fluidreservoir, configuration of optical element, wavelength of light,concentration of slurry, amount of impact on the process, etc. As shown,a slurry 604 that is placed between the pad 607 and the sample 602 issubstantially cleared away from the viewing surface of the sample 602 bythe flowing fluid 613.

The fluid pump 612 may also include a sensor (not shown) arranged todetermine when the sample is near the self-clearing objective. Thesensor may utilize pressure, optical, or other inputs to determinesample location. The fluid flow may then be modulated as the sample isnear or on top of the self-clearing objective. This arrangement clearsthe debris along the optical path without overly diluting the slurryadjacent to the self-clearing objective. This prevents the slurry frombecoming too diluted to effectively polish the sample.

One or more measurement signals 616 may be directed through the opticalelement 610 and the flowing fluid 613 to the sample 602 to be reflected,detected, and analyzed. One or more detectable signals 618 are thenreflected from the sample 602. The measurement and detectable signals616 and 618 are not significantly distorted by the slurry 604, ascompared to other in-situ measurement systems, since the slurry 604 iscleared away from the signal path by fluid 613 of the self-clearingobjective.

Any suitable type and number of optical measurement device may be usedin conjunction with the self-clearing objective 600. By way of specificexamples, a reflectometer system, an ellipsometer system, aninterferometer system, and a photoacoustic system may be used. Theoptical measurement device may be configured in various ways. Thereflectometer may measure reflectivity using multiple incident beamangles or a single beam angle. Additionally, the reflectometer maymeasure reflectivity at various wavelengths or a single wavelength.Likewise, the ellipsometer may be configured to measure at anycombination of multiple angles, a single angle, multiple wavelengths,and a single wavelength.

Several reflectivity measurement apparatus and reflectivity analysistechniques are described in U.S. Pat. No. 5,747,813 by Norton et al andU.S. patent application Ser. No. 09/298,007 filed 22 Apr. 1999 by Wanget al. Several embodiment of ellipsometer apparatus and methods aredescribed in U.S. Pat. No. 5,910,842 by Piwonka-Corle et al.Photoacoustic systems and methods are described in U.S. application Ser.No. 09/028,417 filed 24 Feb. 1998 by Nikoonahad et al. These patents andpatent applications are herein incorporated by reference in theirentirety.

The optical measurement device may also be utilized to predict theendpoint time. It has been found that there is a dip in reflectivitywhen the endpoint is near. FIG. 7 shows four graphs of reflectivityvalues as a function of film thickness removed. As shown, there is a dipin reflectivity present when the film is completely removed. Forexample, there is a dip prior to removal of a 1000 Angstroms thickcopper layer, and another dip present prior to removal of both 1000Angstroms of copper and 300 Angstroms of TaN. Multiple reflectivitycurves may be generated for various film thicknesses and compositionsand operating conditions to determine how long after the reflectivitydip the endpoint occurs. For example, the endpoint may occur 5 secondsafter the dip. One may then polish a little longer than the estimated 5seconds (e.g., 10 seconds) to ensure that the endpoint is reached.Preferably, reflectivity is measured at several angles of incidence sothat the dip may be more readily perceived.

This reflectivity dip provides a readily identifiable marker forestimating the time until endpoint is reached. This estimation procedurerepresents an improvement over conventional estimations of the entirepolishing time from polish start to endpoint. Since it is unlikely thatthe polishing process will follow a same rate during the entirepolishing process, a total polishing time estimation is unlikely to beaccurate. In contrast, estimating the remaining polishing time after thedip is likely to be an accurate indicator of endpoint time since therate is unlikely to change a significant amount in such a short amountof time until the endpoint is reached. The above described techniquesfor determining variations in polishing rate with the eddy probe mayalso be used with the reflectivity dip to determine endpoint. That is,extra time may be added to account for variation in polishing ratesacross the wafer. For example, extra time may be added to ensure thatthe slowest polishing wafer portion reaches endpoint.

Any suitable optical measurement device may be utilized to obtainmultiple angles of incidence. Several embodiments of optical systemshaving multiple angles of incidence are described in theabove-referenced co-pending U.S. patent application Ser. No. 09/396,143and Ser. No. 09/556,238 by Nikoonahad, which are incorporated byreference.

Measurements may be taken with both the eddy current probe 502 andoptical probe 504 to optimize film thickness measurement accuracy. Thatis, measurements are taken with both probes to obtain optimum resultsover a wide range of film thickness. For example, the eddy and opticalprobes together provide a complete range of metallization end pointing.It has been found that eddy probe measurements are sensitive to thickerfilm measurements, such as 200 to 400 A or higher. It has also beenfound that optical measurements are sensitive to a top layer Cuthickness of about 400 A to 500 A or lower. Thus, eddy probemeasurements may be utilized for thick film measurements, while opticalprobe is utilized for thin film measurements. Additionally, it appearsthat the eddy probe is relatively insensitive to the underlying filmpatterns on a sample.

In another embodiment, one endpoint technique is utilized during a fastrate etch, while another is utilized during a slow rate etch. FIGS. 8Athrough 8C illustrate a relatively fast etch. FIG. 8A shows three layersof a sample: a silicon dioxide layer 802, a Ta layer 804 a, and a Culayer 806 a. Prior to etching, the Cu layer 806 a typically has arelatively large thickness as compared with the underlying Ta layer 804a.

FIG. 8B shows the results after etching the Cu at a relatively fastrate. As well known to those skilled in art, this results in ansubstantially uneven Cu layer 806 a. For example, the Cu layer 806 a maybe about 1000 A at its higher point 808. The Cu layer 806 a then maytaper down to a zero thickness at areas 810 a and 810 b. If the endpointof the Cu layer 806 is not accurately detected, the barrier layer Ta 804b may also be etched away along the areas 810 a and 810 b, as shown inFIG. 8C. That is, dishing or corrosion may occur within the Ta layer 804b. Dishing and erosion are undesirable effects that occur when the Cuendpoint is not accurately detected. As a solution, the eddy currentprobe may be utilized to accurately detect the relatively largethickness 808 (FIG. 8B) of the Cu layer 806 before dishing occurs.

In contrast, when a relatively slow etch rate is utilized, the Cu layer858 etches more evenly, as illustrated in FIG. 8D. For example, the Culayer may be about 200 A at its highest point 858. In this case, theoptical probe can be utilized to accurately measure the Cu endpoint,which occurs at a relatively low Cu thickness (e.g., 200 A).

The above described combination of measurement probes may be utilized inany other suitable in-situ tool. For example, both tools may be utilizedwithin a deposition tool. FIG. 9 is a diagrammatic illustration of amulti-chamber deposition tool 900 having a combination eddy current andoptical probe in accordance with one embodiment of the presentinvention.

As shown, the deposition tool 900 has a first chamber 902 a and a secondchamber 902 b. Of course, any number and type of chambers may be used.The first chamber 902 a may be used to deposit a first layer on sample904, and the second chamber 902 b is then used to deposit a second layeron sample 904. In general terms, the sample 904 is mounted over a firstmaterial 906 a within the first chamber 902 a. The first material 906 ais evaporated onto the sample (908 a).

As shown, the eddy probe 914 a may be mounted on the backside of thesample 904 to detect the first layer thickness. The eddy probe 914 a ispreferably capable of measuring the first layer thickness through thesample's backside. Additionally, an optical emitter 916 a and detector918 a may be mounted within the first chamber 902 a. The emitter 916 aemits a signal towards the sample, which signal is reflected from thesample 904 onto detector 918 a.

The second chamber 902 may be similarly configured. As shown, the secondchamber 902 b also includes a second material 906 b which is evaporatedonto the sample 904 (908 b). The second chamber 902 b also includes aneddy probe 914 b and optical emitter/detectors 916 b and 918 b.

The optical emitter/detector is optional, and the deposition tool maysimply include the eddy probes. Preferably, the calibration techniquesdescribed above and/or the Mallory Patent are implemented with the eddyprobes.

Rather than mount the eddy probe in each chamber, a single eddy probemay be mounted within transfer module 910. As shown, an eddy probe 912is placed adjacent to sample 904. Thus, as the sample moves betweenchambers, the film thickness may then be measured. If it is determinedthat the film thickness is inadequate, the sample may the returned to achamber for reapplication of the film. Of course, each probe is alsocoupled with a processing device (not shown) for determining filmthickness.

Although the foregoing invention has been described in some detail forpurposes of clarity of understanding, it will be apparent that certainchanges and modifications may be practiced within the scope of theappended claims. It should be noted that there are many alternative waysof implementing both the process and apparatus of the present invention.

For example, the optical measurements may also be calibrated with thefilm being removed. After copper is significantly polished but stilloptically opaque, it appears substantially like an ideal copper mirror.This copper mirror may then be utilized to adjust for changes inenvironmental conditions, such as a fiber being bent. Additionally, alow value reflectivity object may also be periodically positioned withinthe optical path to provide a low reflectivity reference forcalibration.

The above eddy probe techniques may also be utilized to simply detectthe sample's presence. A piezo sensor may also be embedded within thecarrier, pad, or platen to determine polishing dynamics. For example,since a different sound is produced when the sample is sliding off thecarrier, this slippage may be detected with the piezo sensor. By way ofanother example, the optical system may be mounted within an endoscopytype arrangement within an orbital platen. Additionally, a conductivepolymer contact may be mounted in the pad to non-destructively obtainvarious electrical measurements of the sample, such as sheet resistance.

The optical and eddy probe sensors may also be used together to provideself-calibration. For example, the optical probe may be calibrated byusing a metal mirror surface as a reference. A metal will be a suitablemirror-like surface when the metal layer is almost clear and stilloptically opaque. This point may be determined by the eddy probe.Additionally, the optical measurement device may be used to determinewhen a film is cleared and then to calibrate the eddy probe for makingsubstrate resistivity measurements, instead of film resistivitymeasurements.

Accordingly, the present embodiments are to be considered asillustrative and not restrictive, and the invention is not to be limitedto the details given herein, but may be modified within the scope andequivalents of the appended claims.

1. A method for measuring conductance of a sample using an eddy currentprobe comprising a sensing coil, comprising: (a) with the eddy currentprobe at a first separation from the sample, and with an AC voltage inthe sensing coil, measuring a first voltage pair comprising in-phase andquadrature components of an induced AC voltage in the sensing coil; (b)with the eddy current probe at the first separation from a referencematerial, and with the AC voltage in the sensing coil, measuring asecond voltage pair comprising in-phase and quadrature components of aninduced AC voltage in the sensing coil; (c) calibrating the first signalbased on the measured second signal; (d) performing N repetitious ofoperations (a) and (b), where N is a positive integer, with the eddycurrent probe at a different separation from the sample and referencematerial during each of said repetitions; (e) determining a conductancefunction relating conductance with location along a selected curve; and(f) after operations (a) through (e), processing the calibrated firstvoltage pairs obtained in operations (a) through (c) to generate alift-off curve, determining an intersection voltage pair representingintersection of the lift-off curve with the selected curve, anddetermining the conductance of the sample from the intersection voltagepair and the conductance function.
 2. The method of claim 1, operation(f) further comprising: (g) for each of several eddy current probeseparations from a first reference sample of known conductance, and withan AC voltage in a drive coil, measuring an induced voltage paircomprising in-phase and quadrature components of an induced AC voltagein the sensing coil, and processing said induced voltage pairs togenerate a reference lift-off curve; (h) repeating operation (g) foreach of a number of different reference samples of known coductance; and(i) processing the reference lift-off curves generated during operations(g) and (b) to determine reference intersection voltage pairsrepresenting intersections of the reference lift-off curves with theselected curve, and generating the conductance function from saidreference intersection voltage pairs.